The Expected Number of Zeros of a Stationary Gaussian Process

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The Variance of the Number of Zeros of a Stationary Normal Process

Let x(t) be a separable stationary normal stochastic process with zero mean, covariance function r(r) (with r(0) = 1, for convenience), and spectrum ^(X) having an absolutely continuous component. Let N denote the number of times x(t) crosses the zero level in Q^t^T and write X2 for the second spectral moment JQ\ dF(X) = —r"(0). Then it is well known that the mean of the random variable N is gi...

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ژورنال

عنوان ژورنال: The Annals of Mathematical Statistics

سال: 1965

ISSN: 0003-4851

DOI: 10.1214/aoms/1177700077